Geodesic
An example of a central simple commutative finite-dimensional algebra with an infinite basis of identities
Algebra i logika, Tome 54 (2015) no. 3, pp. 315-325

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In 1993 I. P. Shestakov came up with the question whether there exists a central simple finite-dimensional algebra over a field of characteristic 0, whose identities are not given by a finite set (Dniester Notebook, Question 3.103). In 2012 I. M. Isaev and the author constructed a desired example, giving an affirmative answer to the question posed. Here research into Shestakov's question is continued for the case of commutative algebras. A seven-dimensional central simple commutative algebra over a field of characteristics 0 having no finite basis of identities is exemplified.
Keywords: simple algebra, identity of algebra, basis of identities, infinitely based algebra. 
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     author = {A. V. Kislitsin},
     title = {An example of a~central simple commutative finite-dimensional algebra with an infinite basis of identities},
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A. V. Kislitsin. An example of a central simple commutative finite-dimensional algebra with an infinite basis of identities. Algebra i logika, Tome 54 (2015) no. 3, pp. 315-325. http://geodesic.mathdoc.fr/item/AL_2015_54_3_a1/